检测刚度非线性对双检测微陀螺灵敏度稳定性影响

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (24) : 46-52.

论文

郝淑英1,2李会杰1,2张辰卿1,2张琪昌3 冯晶晶1,2 李磊3

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Influence of sense stiffness nonlinearity on the sensitivity stability of a double-sense micro-gyroscope

HAO Shu-ying 1,2 LI Hui-jie 1,2 ZHANG Chen-qing 1,2 ZHANG Qi-chang 3 FENG Jing-jing 1,2 LI Lei 3

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摘要

为揭示刚度非线性对双检测微陀螺灵敏度稳定性及精度的影响规律，首先利用复指数法求解双检测方程线性稳态响应，其次采用多尺度法对非线性动力学方程进行摄动分析，并考虑科氏力对检测输出的影响，提出了一种有效的处理高维非线性方程耦合项的方法，在此基础上探讨检测刚度非线性对双检测微陀螺的幅频曲线、共振频率偏移的影响规律。研究发现：检测的刚度非线性造成检测一和检测二的幅频曲线出现硬化、振幅跳跃、多解及共振频率偏移等复杂非线性行为，导致微陀螺灵敏度失稳；微陀螺灵敏度的稳定性及失稳的带宽范围对刚度非线性十分敏感，当刚度非线性达到某一值时其微小的增长都会严重影响微陀螺的灵敏度的稳定性并使失稳的带宽范围显著增加，如此会导致线性系统设计的失效。

Abstract

To reveal the influence of stiffness nonlinearity on the stability and accuracy of double-sense micro-gyroscope sensitivity, firstly, the linear response of a double-sense equation was solved by using the complex exponential method.Secondly, the multi-scale method was used to analyze the nonlinear dynamic equation considering the influence of the Coriolis force on the sense output.An effective method to deal with the coupling term of high-dimensional nonlinear equations was proposed.The influence of the sense nonlinearity stiffness on the amplitude-frequency curve and the resonance frequency were studied.It is found that the sense nonlinearity stiffness causes the complex nonlinear behavior such as hardening, amplitude jumping, multiple solutions and resonance frequency shift, which leads to the instability of the micro-gyroscope sensitivity.The stability of the micro-gyroscope sensitivity and the unsteady bandwidth range are very sensitive to stiffness nonlinearity.When the stiffness nonlinearity reaches a certain value, its small growth will also seriously affect the stability of the micro-gyroscope sensitivity and increase the bandwidth instability range, which leads to linear system design failure.

导出引用

郝淑英1,2李会杰1,2张辰卿1,2张琪昌3 冯晶晶1,2 李磊3. 检测刚度非线性对双检测微陀螺灵敏度稳定性影响[J]. 振动与冲击, 2018, 37(24): 46-52

HAO Shu-ying 1,2 LI Hui-jie 1,2 ZHANG Chen-qing 1,2 ZHANG Qi-chang 3 FENG Jing-jing 1,2 LI Lei 3. Influence of sense stiffness nonlinearity on the sensitivity stability of a double-sense micro-gyroscope[J]. Journal of Vibration and Shock, 2018, 37(24): 46-52

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